Localization method for lines of discontinuity of an approximately defined function of two variables |
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Authors: | T V Antonova |
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Institution: | 1. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia
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Abstract: | A function of two variables with lines of discontinuity of the first kind is considered. It is assumed that outside the discontinuity lines the function is smooth and has a bounded partial derivative. An approximation to the function in L 2 and a perturbation level are known. The problem in question belongs to a class of nonlinear ill-posed problems, which are solved by constructing some regularizing algorithms. We propose a simple theoretical approach to solving the problem of localizing the discontinuity lines of a function that is noisy in the space L 2. Some conditions on the exact function are imposed ??in the small.?? Methods of averaging are constructed, and error estimates of localizing the lines (in the small) are obtained. |
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